Factoring polynomial for area and then finding perimeter.

Question

The area of a square in square feet is 4zsqd + 12z + 36. Find the expression for the perimeter of the square. Then find the perimeter when z = 4 ft.

Answer 1

A square is a polygon that has 4 sides of equal length all around.

 

Here is the formula of area and perimeter of a typical square:

 

Area = L²

Perimeter = 4L

 

where L = side length

 

Area = 4z² + 12z + 36

Area = 4(z² + 3z + 9)

 

We need to find the length of the square first in order to find the perimeter.  Simply square-root the given area. 

 

L = √(4(z² + 3z + 9))

 

L = 2√(z² + 3z + 9)

 

 

Multiply L by 4 to obtain the perimeter.

 

Perimeter = 4(2√(z² + 3z + 9))

 

               = 8√(z² + 3z + 9)

 

 

Next, substitute z=4 into the formula of perimeter that was just obtained.